This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##   [1] "beta1_pH"       "re_dsr"         "re_pelagic"     "re_yellow"     
##   [5] "beta0_pH"       "re_pH"          "pDSR_YE_ay"     "p_yellow"      
##   [9] "pDSR_YE_ayu"    "beta3_pH"       "pDSR_YE_ayg"    "beta2_pH"      
##  [13] "mu_beta2_pH"    "mu_beta1_pH"    "re_black"       "p_dsr"         
##  [17] "p_pelagic"      "Hdnye_ay"       "re_slope"       "mu_beta0_pH"   
##  [21] "Hdnye_ayg"      "tau_beta0_pH"   "Rb_ayg"         "Rb_ayg_mort"   
##  [25] "p_black"        "Tb_ayg"         "Hb_ayg"         "Tp_ayg"        
##  [29] "R_ayg"          "Rp_ayg"         "Rp_ayg_mort"    "Rb_ay"         
##  [33] "Bb_ayg"         "Tb_ay"          "Rb_ay_mort"     "R_ay"          
##  [37] "Rp_ay"          "Bb_ay"          "Tp_ay"          "Rp_ay_mort"    
##  [41] "Bp_ay"          "Bp_ayg"         "beta4_pH"       "Bp_ayu"        
##  [45] "Bb_ayu"         "Rb_ayu"         "Rb_ayu_mort"    "Rp_ayu"        
##  [49] "Rp_ayu_mort"    "R_ayu"          "Tb_ayu"         "Tp_ayu"        
##  [53] "Ry_ayg"         "Ry_ayg_mort"    "Ty_ayg"         "By_ayg"        
##  [57] "Ry_ayu"         "Ry_ayu_mort"    "Ry_ay"          "Ry_ay_mort"    
##  [61] "By_ayu"         "By_ay"          "Ty_ay"          "Ty_ayu"        
##  [65] "Hd_ay"          "Rd_ayg"         "Rd_ay"          "Bs_ayu"        
##  [69] "Rd_ayu"         "Rs_ayu"         "Rs_ayu_mort"    "Ts_ayu"        
##  [73] "pH"             "Hd_ayg"         "Hb_ay"          "Bs_ay"         
##  [77] "Rs_ay"          "Rs_ay_mort"     "Ts_ay"          "Htrend_ay"     
##  [81] "Ro_ayu"         "Hb_ayu"         "Hy_ay"          "Hp_ayu"        
##  [85] "Hp_ay"          "Bs_ayg"         "beta_H"         "Rs_ayg"        
##  [89] "Rs_ayg_mort"    "Rdnye_ayu"      "Rdnye_ayu_mort" "Hy_ayg"        
##  [93] "Ro_ay"          "Ro_ayg"         "Rdnye_ay_mort"  "Rdnye_ay"      
##  [97] "Ts_ayg"         "Rdnye_ayg"      "Rdnye_ayg_mort" "pG"            
## [101] "Hdnye_ayu"      "Hd_ayu"         "Tdnye_ayu"      "Bdnye_ayu"     
## [105] "Ho_ayu"         "logbc_H"        "Hy_ayu"         "H_ay"          
## [109] "H_ayu"          "H_ayg"          "Ho_ay"          "Hp_ayg"        
## [113] "tau_beta2_pH"   "Ho_ayg"         "Tdnye_ay"       "Bdnye_ay"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 4 2.708609
beta0_yellow 6 1.901856
beta1_black 2 1.803880
beta1_yellow 6 1.802129
beta0_pelagic 5 1.651826
beta1_pelagic 4 1.618456
beta1_pH 20 1.605636
beta2_pH 9 1.489829
beta0_pH 17 1.476536
mu_beta0_yellow 1 1.340594
tau_beta0_pH 2 1.316206
beta3_pH 14 1.297856
parameter n badRhat_avg
beta2_pelagic 5 1.254529
beta4_pelagic 1 1.240999
beta3_pelagic 5 1.239880
beta2_yellow 2 1.217523
mu_beta0_pH 3 1.197823
beta0_black 2 1.197461
tau_beta0_yellow 2 1.176793
beta_H 7 1.172912
beta3_black 2 1.145282
beta4_yellow 1 1.123079
sd_bc_H 1 1.115738
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta_H 0 0 0 0 0 1 0 6 0 0 0 0 0 0 0 0
beta_H 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
beta0_pH 1 1 1 1 0 1 1 1 1 1 2 0 2 2 1 1
beta0_pH 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1
beta1_pH 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 2
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta2_pH 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1
beta2_pH 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1
beta3_pH 1 1 0 1 0 0 0 0 1 1 2 1 1 1 2 2
beta3_pH 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1
beta4_pH 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0
Bp_ay 0 0 0 0 0 0 0 0 0 0 12 11 12 13 12 28
Bp_ayg 0 0 0 0 0 0 0 0 0 0 13 11 12 13 12 18
Bp_ayu 0 0 0 0 0 0 0 0 0 0 10 11 10 13 12 26
H_ay 0 0 0 0 0 1 0 7 0 0 0 0 5 0 0 0
H_ayg 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0
H_ayu 0 0 0 0 0 1 0 6 0 0 0 0 5 0 0 0
Hb_ay 0 0 7 0 0 0 0 4 0 0 0 0 1 0 0 26
Hb_ayg 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 6
Hb_ayu 0 0 1 0 0 0 0 5 0 0 0 0 0 0 0 29
Hd_ay 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 2
Hd_ayg 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0 0
Hd_ayu 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 0
Hdnye_ayg 0 0 0 0 0 0 0 0 0 0 3 0 0 4 0 0
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 0
Ho_ay 0 0 0 0 3 0 0 1 0 0 0 0 0 0 0 0
Ho_ayg 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
Ho_ayu 0 0 0 0 4 0 0 0 1 0 0 0 0 0 0 0
Hp_ay 0 0 11 0 0 0 0 5 0 0 0 0 0 0 0 26
Hp_ayg 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 6
Hp_ayu 0 0 5 0 1 0 0 5 0 0 0 0 0 0 0 29
Htrend_ay 0 0 0 0 0 0 0 17 0 0 0 0 12 0 0 0
Hy_ay 0 0 0 0 0 0 0 5 0 0 3 0 0 2 0 2
Hy_ayg 0 0 0 0 1 0 0 0 0 0 1 0 0 2 0 1
Hy_ayu 0 0 0 0 0 0 0 5 4 0 2 0 0 0 0 2
logbc_H 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0
mu_beta0_pH 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta1_pH 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta2_pH 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_black 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 4 5 0 2 0 0
p_pelagic 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 50
p_yellow 0 0 0 0 0 0 0 0 0 0 4 0 0 8 0 6
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 3 0 0 4 0 3
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 3
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 3
pG 0 0 0 0 0 3 0 0 0 0 0 0 5 0 0 0
pH 0 40 4 1 6 0 0 6 0 0 4 0 24 2 0 1
R_ay 12 10 8 11 14 16 11 11 12 12 12 11 12 13 12 11
R_ayg 12 12 10 11 10 14 9 12 12 12 13 12 11 13 11 12
R_ayu 11 7 11 11 14 17 14 12 7 10 9 12 8 13 12 10
Rb_ay 13 37 12 13 15 18 12 14 12 12 16 12 27 13 12 11
Rb_ay_mort 13 38 11 13 15 18 12 14 12 12 16 12 27 13 12 11
Rb_ayg 13 22 10 13 12 14 9 14 12 12 14 12 18 13 11 12
Rb_ayg_mort 13 22 10 13 12 14 9 14 12 12 14 12 18 13 11 12
Rb_ayu 13 41 15 15 16 19 15 13 7 10 15 12 23 15 11 12
Rb_ayu_mort 13 41 15 15 16 19 15 13 7 10 15 12 23 15 11 12
Rd_ay 0 0 0 0 0 0 0 0 0 0 4 6 8 8 4 4
Rd_ayg 0 0 0 0 0 0 0 0 0 0 9 7 10 9 6 8
Rd_ayu 0 0 0 0 0 0 0 0 0 0 0 4 7 4 3 1
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 18 1 1 0 0
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 18 1 1 0 0
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 4 10 0 1 0 0
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 4 10 0 1 0 0
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 19 1 2 0 0
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 19 1 2 0 0
re_pelagic 0 0 5 0 0 0 0 0 0 0 14 0 7 7 0 39
re_pH 25 25 25 25 0 26 25 25 21 12 43 14 27 30 18 39
re_slope 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
Ro_ay 1 1 0 0 4 2 2 2 1 1 1 20 1 1 0 0
Ro_ayg 0 2 3 5 0 2 3 3 1 0 4 10 0 1 0 0
Ro_ayu 1 1 0 1 4 2 2 2 1 1 2 20 1 1 1 0
Rp_ay 12 40 11 13 15 19 12 14 12 12 17 12 25 13 13 11
Rp_ay_mort 12 40 12 14 15 19 12 14 12 12 17 12 25 13 13 11
Rp_ayg 12 21 10 13 10 14 9 12 12 12 14 12 17 13 11 12
Rp_ayg_mort 12 21 10 13 10 14 9 12 12 12 14 12 17 13 11 12
Rp_ayu 11 41 14 14 15 20 15 14 7 10 15 12 23 14 13 12
Rp_ayu_mort 11 41 14 14 15 20 15 14 7 10 15 12 23 14 13 12
Rs_ay 0 0 0 0 0 0 0 0 0 0 1 25 0 1 1 0
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 1 25 0 1 1 0
Rs_ayg 0 0 0 0 0 0 0 0 0 0 4 8 0 2 0 1
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 4 8 0 2 0 1
Rs_ayu 0 0 0 0 0 0 0 0 0 0 4 28 0 1 2 0
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 4 28 0 1 2 0
Ry_ay 4 7 3 12 27 24 7 5 10 6 4 6 11 9 5 5
Ry_ay_mort 4 6 3 12 27 24 6 5 10 6 4 6 11 9 5 5
Ry_ayg 13 11 8 12 19 13 8 14 11 14 9 8 10 8 6 8
Ry_ayg_mort 13 11 8 12 19 13 8 14 11 14 9 8 10 8 6 8
Ry_ayu 4 5 3 6 28 24 11 5 10 6 0 4 6 5 3 2
Ry_ayu_mort 4 5 3 6 28 24 11 5 10 6 0 4 6 5 3 2
tau_beta0_pH 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta2_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ay 12 6 8 10 12 13 10 15 11 12 12 11 13 13 12 27
Tp_ayg 12 4 10 10 9 13 9 13 11 12 13 11 12 13 11 19
Tp_ayu 10 3 8 8 12 12 14 16 7 10 10 11 8 13 12 26
beta0_black 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1
beta0_yellow 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1
beta1_black 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta1_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1
beta1_yellow 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1
beta2_pelagic 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1
beta2_yellow 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta3_black 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta3_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1
beta3_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta4_yellow 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
mu_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
sd_bc_H 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
tau_beta0_yellow 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.148 0.076 -0.286 -0.152 0.016
mu_bc_H[2] -0.123 0.040 -0.200 -0.124 -0.044
mu_bc_H[3] -0.463 0.069 -0.589 -0.465 -0.319
mu_bc_H[4] -1.065 0.199 -1.471 -1.065 -0.686
mu_bc_H[5] 0.666 0.933 -0.386 0.509 2.579
mu_bc_H[6] -2.191 0.343 -2.847 -2.193 -1.533
mu_bc_H[7] -0.496 0.110 -0.719 -0.492 -0.286
mu_bc_H[8] 0.073 0.288 -0.401 0.040 0.741
mu_bc_H[9] -0.352 0.142 -0.645 -0.347 -0.086
mu_bc_H[10] -0.135 0.069 -0.261 -0.138 0.009
mu_bc_H[11] -0.142 0.042 -0.227 -0.141 -0.061
mu_bc_H[12] -0.268 0.114 -0.513 -0.261 -0.065
mu_bc_H[13] -0.235 0.081 -0.395 -0.233 -0.080
mu_bc_H[14] -0.361 0.106 -0.588 -0.355 -0.167
mu_bc_H[15] -0.374 0.055 -0.481 -0.375 -0.266
mu_bc_H[16] -0.675 0.355 -1.338 -0.684 0.067
mu_bc_R[1] 1.474 0.149 1.184 1.475 1.766
mu_bc_R[2] 1.523 0.089 1.353 1.522 1.699
mu_bc_R[3] 1.449 0.147 1.152 1.450 1.735
mu_bc_R[4] 1.107 0.181 0.730 1.114 1.452
mu_bc_R[5] 1.643 0.513 0.609 1.639 2.669
mu_bc_R[6] -0.954 0.534 -1.998 -0.949 0.082
mu_bc_R[7] 0.441 0.154 0.128 0.443 0.744
mu_bc_R[8] 0.569 0.189 0.210 0.568 0.939
mu_bc_R[9] 0.531 0.170 0.177 0.538 0.843
mu_bc_R[10] 1.510 0.128 1.252 1.511 1.757
mu_bc_R[11] 1.058 0.115 0.845 1.054 1.283
mu_bc_R[12] 0.932 0.204 0.531 0.928 1.333
mu_bc_R[13] 1.108 0.109 0.905 1.104 1.340
mu_bc_R[14] 0.950 0.150 0.656 0.950 1.237
mu_bc_R[15] 0.892 0.120 0.670 0.888 1.147
mu_bc_R[16] 1.157 0.132 0.911 1.153 1.423
tau_pH[1] 0.128 0.155 0.040 0.065 0.623
tau_pH[2] 1.428 0.767 0.185 1.784 2.372
tau_pH[3] 2.044 0.446 0.819 2.077 2.829
beta0_pH[1,1] 4.163 1.557 1.806 3.987 7.634
beta0_pH[2,1] 10.196 3.264 3.549 9.960 15.773
beta0_pH[3,1] 5.705 2.295 2.346 5.617 10.590
beta0_pH[4,1] 4.723 1.926 2.494 4.140 10.292
beta0_pH[5,1] 2.082 0.920 0.540 1.989 3.982
beta0_pH[6,1] 1.461 0.702 0.212 1.418 2.844
beta0_pH[7,1] 2.480 1.374 0.618 2.418 6.148
beta0_pH[8,1] 2.526 1.317 0.542 2.417 5.030
beta0_pH[9,1] 2.179 1.048 0.720 1.850 4.391
beta0_pH[10,1] 3.424 1.428 1.557 3.051 6.007
beta0_pH[11,1] 7.223 1.778 3.592 7.116 9.962
beta0_pH[12,1] 3.964 1.313 1.892 3.657 6.691
beta0_pH[13,1] 7.227 2.389 1.746 7.877 11.082
beta0_pH[14,1] 3.053 1.370 1.257 2.684 6.038
beta0_pH[15,1] 6.755 1.839 2.228 7.373 9.358
beta0_pH[16,1] 6.221 2.688 1.725 6.383 11.777
beta0_pH[1,2] 2.871 0.236 2.427 2.863 3.392
beta0_pH[2,2] 2.866 0.198 2.450 2.870 3.266
beta0_pH[3,2] 3.144 0.222 2.760 3.120 3.672
beta0_pH[4,2] 3.043 0.252 2.679 2.997 3.728
beta0_pH[5,2] 4.723 1.463 2.844 4.387 8.487
beta0_pH[6,2] 3.180 0.327 2.643 3.151 3.955
beta0_pH[7,2] 1.849 0.306 1.263 1.845 2.535
beta0_pH[8,2] 2.914 0.305 2.381 2.892 3.635
beta0_pH[9,2] 3.509 0.351 2.918 3.475 4.305
beta0_pH[10,2] 3.650 0.299 3.119 3.630 4.336
beta0_pH[11,2] -2.473 3.271 -5.373 -4.421 5.641
beta0_pH[12,2] -3.273 2.218 -5.330 -4.434 1.234
beta0_pH[13,2] -3.091 2.285 -5.189 -4.253 1.413
beta0_pH[14,2] -3.629 2.597 -5.980 -5.048 1.250
beta0_pH[15,2] -2.673 2.363 -4.792 -4.004 2.013
beta0_pH[16,2] -3.165 2.466 -5.394 -4.475 1.842
beta0_pH[1,3] -0.591 0.796 -2.259 -0.549 0.880
beta0_pH[2,3] 2.202 0.171 1.874 2.195 2.544
beta0_pH[3,3] 2.513 0.157 2.203 2.513 2.816
beta0_pH[4,3] 2.964 0.169 2.638 2.961 3.310
beta0_pH[5,3] 1.050 0.604 0.201 0.960 2.392
beta0_pH[6,3] 0.633 0.577 -0.527 0.682 1.656
beta0_pH[7,3] 0.680 0.192 0.322 0.675 1.077
beta0_pH[8,3] 0.321 0.202 -0.062 0.322 0.736
beta0_pH[9,3] -0.435 0.406 -1.222 -0.450 0.468
beta0_pH[10,3] 0.527 0.372 -0.372 0.556 1.156
beta0_pH[11,3] -0.181 0.710 -1.175 -0.289 1.621
beta0_pH[12,3] -0.753 0.828 -1.761 -0.900 1.897
beta0_pH[13,3] -0.086 0.699 -1.306 -0.137 1.507
beta0_pH[14,3] -0.151 0.531 -0.831 -0.258 1.530
beta0_pH[15,3] -0.415 1.307 -2.109 -0.682 3.182
beta0_pH[16,3] -0.303 0.653 -1.249 -0.417 1.269
beta1_pH[1,1] 0.195 0.444 0.000 0.000 1.573
beta1_pH[2,1] 0.214 0.504 0.000 0.000 1.766
beta1_pH[3,1] 0.147 0.489 0.000 0.000 1.436
beta1_pH[4,1] 0.273 0.672 0.000 0.000 2.648
beta1_pH[5,1] 0.274 0.674 0.000 0.000 2.281
beta1_pH[6,1] 0.217 0.570 0.000 0.000 2.067
beta1_pH[7,1] 0.364 0.782 0.000 0.000 2.596
beta1_pH[8,1] 0.371 0.764 0.000 0.000 2.640
beta1_pH[9,1] 0.286 0.657 0.000 0.000 2.298
beta1_pH[10,1] 0.591 0.815 0.000 0.000 2.177
beta1_pH[11,1] 1.705 1.800 0.000 0.885 4.861
beta1_pH[12,1] 0.411 0.714 0.000 0.015 2.654
beta1_pH[13,1] 0.201 0.374 0.000 0.009 1.341
beta1_pH[14,1] 0.199 0.381 0.000 0.009 1.393
beta1_pH[15,1] 0.110 0.273 0.000 0.005 1.012
beta1_pH[16,1] 0.199 0.411 0.000 0.009 1.460
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.001 0.000 0.000 0.001
beta1_pH[4,2] 0.004 0.037 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 4.443 2.707 0.000 6.102 7.113
beta1_pH[12,2] 4.680 2.529 0.000 5.985 6.981
beta1_pH[13,2] 5.056 2.837 0.000 6.560 7.570
beta1_pH[14,2] 5.070 2.871 0.000 6.658 7.657
beta1_pH[15,2] 4.799 2.793 0.000 6.392 7.274
beta1_pH[16,2] 5.356 2.969 0.000 6.953 7.970
beta1_pH[1,3] 5.311 1.682 2.210 5.306 8.511
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 4.498 7.823 1.148 2.725 35.343
beta1_pH[6,3] 2.432 2.470 0.430 2.107 5.907
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.693 0.377 1.925 2.704 3.412
beta1_pH[9,3] 2.567 0.445 1.703 2.573 3.473
beta1_pH[10,3] 2.786 0.502 1.882 2.763 3.906
beta1_pH[11,3] 2.660 1.003 0.000 2.878 3.929
beta1_pH[12,3] 3.900 1.182 0.000 4.140 5.211
beta1_pH[13,3] 1.583 0.721 0.000 1.706 2.711
beta1_pH[14,3] 2.348 0.744 0.000 2.502 3.245
beta1_pH[15,3] 1.770 0.982 0.000 1.944 3.427
beta1_pH[16,3] 1.654 0.730 0.000 1.822 2.658
beta2_pH[1,1] 1.708 9.920 -18.340 1.750 21.433
beta2_pH[2,1] 1.267 9.799 -18.410 0.033 20.808
beta2_pH[3,1] 1.497 9.895 -18.202 1.505 21.514
beta2_pH[4,1] 1.594 9.925 -18.783 1.071 21.437
beta2_pH[5,1] -0.163 2.798 -6.312 -0.072 5.808
beta2_pH[6,1] -0.440 2.717 -6.408 -0.256 5.352
beta2_pH[7,1] 0.068 1.706 0.000 0.000 0.077
beta2_pH[8,1] -0.211 2.766 -6.078 -0.187 5.827
beta2_pH[9,1] -0.210 2.643 -5.943 -0.199 5.425
beta2_pH[10,1] -0.719 2.102 -5.279 -0.686 4.502
beta2_pH[11,1] 7.218 9.494 -9.204 4.870 32.757
beta2_pH[12,1] 6.686 9.336 -9.855 4.267 30.782
beta2_pH[13,1] 6.729 9.292 -9.922 4.567 29.706
beta2_pH[14,1] 6.652 9.250 -9.378 4.406 29.858
beta2_pH[15,1] 6.633 9.417 -9.578 4.468 29.683
beta2_pH[16,1] 5.952 9.715 -10.364 3.985 30.527
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.025 1.883 -6.792 -1.498 -0.029
beta2_pH[4,2] -2.019 1.820 -6.582 -1.524 -0.030
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.756 6.688 -24.140 -9.136 3.883
beta2_pH[12,2] -9.073 6.797 -23.606 -8.468 3.501
beta2_pH[13,2] -8.878 6.830 -23.478 -8.139 4.286
beta2_pH[14,2] -9.160 6.767 -23.855 -8.567 4.494
beta2_pH[15,2] -9.605 6.611 -24.002 -9.015 4.161
beta2_pH[16,2] -9.835 6.572 -23.325 -9.211 3.821
beta2_pH[1,3] 0.170 0.116 0.100 0.137 0.432
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.305 5.878 0.891 8.358 23.213
beta2_pH[6,3] 9.137 6.178 0.195 8.363 23.167
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.071 5.695 1.785 9.037 23.463
beta2_pH[9,3] 9.328 5.958 0.774 8.478 23.062
beta2_pH[10,3] 8.692 6.235 0.497 7.985 23.026
beta2_pH[11,3] -2.311 3.300 -12.345 -1.493 -0.403
beta2_pH[12,3] -2.426 3.171 -11.150 -1.713 -0.714
beta2_pH[13,3] -2.642 3.346 -12.193 -1.826 0.319
beta2_pH[14,3] -2.826 3.352 -11.901 -1.980 -0.690
beta2_pH[15,3] -2.648 3.541 -12.704 -1.942 2.752
beta2_pH[16,3] -2.846 3.368 -12.053 -1.999 0.308
beta3_pH[1,1] 31.313 7.359 18.732 31.520 44.365
beta3_pH[2,1] 32.611 7.744 18.979 32.667 45.310
beta3_pH[3,1] 29.939 7.591 18.472 29.295 44.735
beta3_pH[4,1] 25.708 6.444 18.263 24.197 43.043
beta3_pH[5,1] 29.561 7.931 18.344 28.497 44.802
beta3_pH[6,1] 30.202 8.219 18.488 29.199 45.033
beta3_pH[7,1] 30.365 7.941 18.515 29.705 45.022
beta3_pH[8,1] 27.536 7.220 18.428 25.444 43.788
beta3_pH[9,1] 30.007 8.009 18.462 28.409 44.909
beta3_pH[10,1] 32.490 7.679 18.772 33.210 45.413
beta3_pH[11,1] 36.366 3.545 30.060 35.738 43.994
beta3_pH[12,1] 37.205 4.978 29.332 37.175 45.553
beta3_pH[13,1] 36.287 4.824 29.349 35.739 45.319
beta3_pH[14,1] 33.421 3.999 29.141 32.081 44.445
beta3_pH[15,1] 34.776 4.556 29.139 34.072 44.898
beta3_pH[16,1] 35.218 4.514 29.232 34.441 44.770
beta3_pH[1,2] 30.110 7.977 18.484 29.052 44.992
beta3_pH[2,2] 30.238 7.956 18.459 29.587 45.052
beta3_pH[3,2] 29.767 7.972 18.456 28.720 44.745
beta3_pH[4,2] 29.786 7.962 18.440 28.755 44.744
beta3_pH[5,2] 30.004 8.071 18.439 28.851 44.982
beta3_pH[6,2] 29.908 7.725 18.582 29.051 44.540
beta3_pH[7,2] 30.021 7.849 18.483 29.416 44.949
beta3_pH[8,2] 29.970 7.887 18.546 29.127 44.720
beta3_pH[9,2] 30.012 7.877 18.433 29.163 44.750
beta3_pH[10,2] 29.794 7.964 18.415 28.681 45.064
beta3_pH[11,2] 41.703 3.586 30.912 43.330 43.938
beta3_pH[12,2] 41.830 3.356 30.848 43.110 43.910
beta3_pH[13,2] 42.403 3.557 30.778 43.881 44.130
beta3_pH[14,2] 41.710 3.408 30.769 43.153 43.860
beta3_pH[15,2] 41.974 3.467 30.666 43.323 43.941
beta3_pH[16,2] 42.144 3.429 30.932 43.446 43.940
beta3_pH[1,3] 38.151 4.028 30.148 38.128 45.436
beta3_pH[2,3] 30.398 7.936 18.596 29.711 44.993
beta3_pH[3,3] 30.072 8.002 18.387 29.287 44.924
beta3_pH[4,3] 30.200 8.001 18.450 29.591 44.971
beta3_pH[5,3] 40.931 3.556 32.366 41.965 45.533
beta3_pH[6,3] 37.784 4.771 31.199 38.304 45.493
beta3_pH[7,3] 38.120 4.275 31.308 37.899 45.546
beta3_pH[8,3] 41.488 0.307 40.999 41.505 41.955
beta3_pH[9,3] 33.580 0.540 32.446 33.607 34.556
beta3_pH[10,3] 35.891 0.769 33.562 36.028 36.886
beta3_pH[11,3] 41.435 2.183 32.802 41.924 43.445
beta3_pH[12,3] 41.475 1.821 34.528 41.797 42.765
beta3_pH[13,3] 42.429 3.091 31.674 42.912 45.852
beta3_pH[14,3] 40.812 1.801 33.958 41.113 42.294
beta3_pH[15,3] 41.242 3.731 30.035 42.619 44.244
beta3_pH[16,3] 42.266 2.763 31.550 42.974 44.870
beta0_pelagic[1] 2.201 0.126 1.958 2.205 2.456
beta0_pelagic[2] 1.505 0.139 1.264 1.498 1.792
beta0_pelagic[3] -0.182 0.637 -1.611 0.019 0.667
beta0_pelagic[4] 0.305 0.248 -0.279 0.316 0.790
beta0_pelagic[5] 1.156 0.248 0.686 1.158 1.642
beta0_pelagic[6] 1.435 0.296 0.792 1.467 1.948
beta0_pelagic[7] 1.619 0.237 1.183 1.604 2.155
beta0_pelagic[8] 1.727 0.204 1.324 1.723 2.151
beta0_pelagic[9] 2.444 0.327 1.824 2.432 3.071
beta0_pelagic[10] 2.472 0.213 2.009 2.492 2.846
beta0_pelagic[11] -0.544 0.282 -1.158 -0.513 -0.015
beta0_pelagic[12] 1.660 0.144 1.377 1.658 1.939
beta0_pelagic[13] 0.189 0.173 -0.181 0.183 0.519
beta0_pelagic[14] -0.051 0.190 -0.397 -0.061 0.334
beta0_pelagic[15] -0.313 0.170 -0.588 -0.336 0.038
beta0_pelagic[16] -0.022 0.404 -0.956 0.108 0.498
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.536 0.977 0.295 1.172 3.608
beta1_pelagic[4] 0.979 0.270 0.476 0.971 1.594
beta1_pelagic[5] -0.088 0.303 -0.689 -0.084 0.488
beta1_pelagic[6] -0.163 0.510 -0.953 -0.272 0.781
beta1_pelagic[7] -0.004 0.317 -0.616 -0.010 0.628
beta1_pelagic[8] -0.024 0.275 -0.556 -0.023 0.510
beta1_pelagic[9] 0.252 0.502 -0.767 0.383 0.975
beta1_pelagic[10] 0.053 0.270 -0.475 0.055 0.576
beta1_pelagic[11] 3.471 0.716 1.965 3.611 4.663
beta1_pelagic[12] 2.880 0.320 2.307 2.859 3.549
beta1_pelagic[13] 3.166 0.584 2.195 3.128 4.552
beta1_pelagic[14] 4.294 1.016 2.688 4.170 6.263
beta1_pelagic[15] 2.895 0.307 2.286 2.883 3.489
beta1_pelagic[16] 3.923 0.945 2.731 3.677 6.208
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 1.074 2.826 0.050 0.249 9.451
beta2_pelagic[4] 2.409 4.191 0.099 0.749 16.706
beta2_pelagic[5] -0.030 0.676 -1.411 -0.044 1.413
beta2_pelagic[6] -0.157 0.708 -1.536 -0.225 1.306
beta2_pelagic[7] -0.012 0.652 -1.435 0.000 1.344
beta2_pelagic[8] 0.074 0.565 -1.215 0.087 1.279
beta2_pelagic[9] 0.240 0.687 -1.237 0.295 1.602
beta2_pelagic[10] 0.019 0.610 -1.307 0.023 1.253
beta2_pelagic[11] 0.239 0.244 0.131 0.193 0.497
beta2_pelagic[12] 3.902 2.866 0.939 3.177 11.386
beta2_pelagic[13] 0.553 0.593 0.194 0.389 2.327
beta2_pelagic[14] 0.329 0.123 0.178 0.302 0.658
beta2_pelagic[15] 3.767 2.561 1.298 3.053 10.455
beta2_pelagic[16] 1.244 1.609 0.153 0.546 5.752
beta3_pelagic[1] 29.866 7.791 18.501 28.704 44.544
beta3_pelagic[2] 29.976 7.802 18.469 29.313 44.534
beta3_pelagic[3] 29.625 5.152 19.826 29.598 41.124
beta3_pelagic[4] 26.452 4.018 20.895 25.791 39.565
beta3_pelagic[5] 29.981 8.133 18.544 28.710 45.203
beta3_pelagic[6] 32.026 6.200 19.493 31.808 43.808
beta3_pelagic[7] 29.475 7.742 18.519 28.280 44.770
beta3_pelagic[8] 29.933 8.016 18.422 28.849 44.859
beta3_pelagic[9] 30.991 5.876 19.614 30.952 42.677
beta3_pelagic[10] 29.289 8.133 18.470 27.787 45.097
beta3_pelagic[11] 36.493 2.398 30.560 36.516 40.846
beta3_pelagic[12] 43.460 0.289 42.953 43.453 44.000
beta3_pelagic[13] 42.850 1.184 40.750 42.793 45.243
beta3_pelagic[14] 42.584 1.410 40.104 42.393 45.511
beta3_pelagic[15] 43.033 0.329 42.236 43.096 43.581
beta3_pelagic[16] 42.237 1.476 38.004 42.573 44.907
mu_beta0_pelagic[1] 0.870 0.930 -1.133 0.926 2.705
mu_beta0_pelagic[2] 1.781 0.371 1.001 1.791 2.539
mu_beta0_pelagic[3] 0.149 0.505 -0.914 0.162 1.157
tau_beta0_pelagic[1] 0.631 0.650 0.057 0.417 2.337
tau_beta0_pelagic[2] 2.967 3.346 0.275 2.053 11.294
tau_beta0_pelagic[3] 1.265 0.951 0.158 1.027 3.617
beta0_yellow[1] -0.557 0.208 -1.080 -0.532 -0.219
beta0_yellow[2] 0.498 0.153 0.182 0.498 0.800
beta0_yellow[3] -0.320 0.178 -0.690 -0.322 0.046
beta0_yellow[4] 0.841 0.271 0.026 0.880 1.236
beta0_yellow[5] -0.369 0.349 -1.062 -0.365 0.324
beta0_yellow[6] 1.108 0.163 0.792 1.105 1.434
beta0_yellow[7] 1.016 0.164 0.708 1.010 1.351
beta0_yellow[8] 0.990 0.148 0.703 0.988 1.278
beta0_yellow[9] 0.653 0.160 0.340 0.652 0.971
beta0_yellow[10] 0.592 0.141 0.308 0.594 0.869
beta0_yellow[11] -1.069 0.764 -2.343 -1.178 0.108
beta0_yellow[12] -3.523 0.498 -4.551 -3.501 -2.616
beta0_yellow[13] -3.661 0.685 -4.799 -3.712 -2.190
beta0_yellow[14] -1.135 0.894 -2.535 -1.325 0.147
beta0_yellow[15] -2.154 0.589 -2.994 -2.282 -0.929
beta0_yellow[16] -1.745 0.689 -2.859 -1.864 -0.235
beta1_yellow[1] 0.642 0.484 0.006 0.587 1.765
beta1_yellow[2] 0.997 0.293 0.537 0.968 1.687
beta1_yellow[3] 0.690 0.251 0.230 0.682 1.171
beta1_yellow[4] 1.302 0.578 0.641 1.161 2.803
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 1.315 0.728 0.002 1.373 2.613
beta1_yellow[12] 2.331 0.530 1.314 2.319 3.429
beta1_yellow[13] 2.807 0.695 1.409 2.845 3.952
beta1_yellow[14] 1.208 0.907 0.000 1.413 2.606
beta1_yellow[15] 1.438 0.570 0.028 1.573 2.223
beta1_yellow[16] 1.495 0.704 0.001 1.617 2.599
beta2_yellow[1] -3.179 2.798 -10.392 -2.378 -0.028
beta2_yellow[2] -2.759 2.329 -9.031 -1.920 -0.215
beta2_yellow[3] -3.057 2.677 -9.867 -2.199 -0.220
beta2_yellow[4] -2.590 2.586 -9.189 -1.722 -0.120
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -5.108 2.924 -12.414 -4.491 -1.052
beta2_yellow[12] -5.425 2.966 -13.284 -4.781 -1.438
beta2_yellow[13] -5.112 2.668 -11.672 -4.477 -1.608
beta2_yellow[14] -4.898 2.882 -11.858 -4.434 -0.755
beta2_yellow[15] -5.190 2.954 -12.366 -4.557 -1.197
beta2_yellow[16] -5.451 2.980 -12.965 -4.808 -1.348
beta3_yellow[1] 27.270 7.616 18.344 24.353 45.015
beta3_yellow[2] 29.384 1.697 26.622 29.161 32.945
beta3_yellow[3] 32.637 2.962 24.700 32.820 37.691
beta3_yellow[4] 29.350 3.401 23.142 28.219 36.030
beta3_yellow[5] 29.867 8.005 18.434 28.766 45.029
beta3_yellow[6] 30.166 7.862 18.514 29.473 44.850
beta3_yellow[7] 29.947 7.914 18.469 28.927 45.081
beta3_yellow[8] 30.272 8.010 18.546 29.379 45.026
beta3_yellow[9] 29.876 7.915 18.472 29.040 44.813
beta3_yellow[10] 30.217 7.995 18.440 29.386 45.089
beta3_yellow[11] 41.507 4.918 33.141 44.379 45.898
beta3_yellow[12] 43.286 0.418 42.369 43.263 44.080
beta3_yellow[13] 44.875 0.425 43.925 44.964 45.552
beta3_yellow[14] 41.375 4.096 33.402 43.580 45.653
beta3_yellow[15] 43.661 2.943 34.644 44.715 45.888
beta3_yellow[16] 43.884 2.169 35.431 44.351 45.825
mu_beta0_yellow[1] 0.097 0.560 -1.077 0.116 1.161
mu_beta0_yellow[2] 0.618 0.359 -0.173 0.640 1.298
mu_beta0_yellow[3] -1.792 0.809 -3.109 -1.891 0.039
tau_beta0_yellow[1] 1.830 2.516 0.096 1.170 6.884
tau_beta0_yellow[2] 3.030 3.417 0.288 2.101 10.891
tau_beta0_yellow[3] 0.723 0.812 0.065 0.443 3.000
beta0_black[1] -0.039 0.168 -0.362 -0.041 0.288
beta0_black[2] 1.916 0.128 1.668 1.916 2.165
beta0_black[3] 1.319 0.135 1.063 1.317 1.584
beta0_black[4] 2.429 0.135 2.167 2.429 2.700
beta0_black[5] 4.588 2.039 1.751 4.154 9.605
beta0_black[6] 4.652 1.977 2.250 4.185 10.030
beta0_black[7] 3.721 1.873 1.565 3.216 8.787
beta0_black[8] 0.921 0.213 0.530 0.914 1.364
beta0_black[9] 2.602 0.236 2.123 2.601 3.069
beta0_black[10] 1.457 0.132 1.195 1.458 1.715
beta0_black[11] 3.481 0.154 3.175 3.480 3.794
beta0_black[12] 4.867 0.175 4.527 4.865 5.213
beta0_black[13] -0.050 0.286 -0.629 -0.045 0.492
beta0_black[14] 2.858 0.159 2.543 2.859 3.164
beta0_black[15] 1.294 0.159 0.980 1.295 1.602
beta0_black[16] 4.273 0.165 3.955 4.271 4.597
beta2_black[1] 8.913 11.075 0.517 3.993 42.409
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.052 1.681 -6.782 -1.503 -0.308
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.605 1.314 38.932 41.866 43.251
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.112 1.046 36.570 39.260 40.562
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.265 0.196 -0.647 -0.264 0.131
beta4_black[2] 0.244 0.186 -0.112 0.246 0.605
beta4_black[3] -0.935 0.194 -1.315 -0.935 -0.575
beta4_black[4] 0.425 0.219 -0.002 0.423 0.851
beta4_black[5] 0.564 1.400 -1.291 0.358 3.603
beta4_black[6] 0.536 1.363 -1.300 0.352 3.625
beta4_black[7] 0.484 1.348 -1.380 0.280 3.511
beta4_black[8] -0.214 0.321 -0.853 -0.204 0.383
beta4_black[9] 0.819 0.775 -0.274 0.668 2.737
beta4_black[10] 0.056 0.182 -0.294 0.051 0.416
beta4_black[11] -0.688 0.215 -1.115 -0.686 -0.270
beta4_black[12] 0.172 0.324 -0.435 0.164 0.819
beta4_black[13] -1.180 0.223 -1.615 -1.182 -0.747
beta4_black[14] -0.190 0.240 -0.640 -0.196 0.282
beta4_black[15] -0.892 0.218 -1.317 -0.886 -0.486
beta4_black[16] -0.596 0.229 -1.064 -0.594 -0.167
mu_beta0_black[1] 1.274 0.925 -0.767 1.308 3.089
mu_beta0_black[2] 2.689 1.063 0.674 2.591 5.071
mu_beta0_black[3] 2.491 1.002 0.290 2.558 4.337
tau_beta0_black[1] 0.635 0.605 0.054 0.439 2.283
tau_beta0_black[2] 0.436 0.558 0.046 0.236 1.963
tau_beta0_black[3] 0.249 0.168 0.050 0.206 0.667
beta0_dsr[11] -3.332 0.952 -5.573 -2.944 -2.381
beta0_dsr[12] 4.535 0.295 3.973 4.535 5.101
beta0_dsr[13] -1.387 0.300 -2.026 -1.377 -0.849
beta0_dsr[14] -3.914 0.543 -5.030 -3.899 -2.966
beta0_dsr[15] -1.929 0.269 -2.447 -1.944 -1.375
beta0_dsr[16] -3.036 0.380 -3.794 -3.028 -2.309
beta1_dsr[11] 5.420 1.171 4.306 4.916 8.146
beta1_dsr[12] 9.401 23.530 2.271 5.248 36.004
beta1_dsr[13] 2.914 0.331 2.350 2.893 3.535
beta1_dsr[14] 6.580 0.567 5.569 6.569 7.756
beta1_dsr[15] 3.361 0.272 2.825 3.365 3.878
beta1_dsr[16] 5.858 0.396 5.095 5.849 6.657
beta2_dsr[11] -5.856 3.948 -13.117 -6.526 -0.328
beta2_dsr[12] -6.524 2.800 -12.709 -6.315 -1.799
beta2_dsr[13] -5.826 2.800 -11.829 -5.559 -1.249
beta2_dsr[14] -5.768 2.719 -12.039 -5.553 -1.614
beta2_dsr[15] -7.477 2.545 -13.097 -7.143 -3.529
beta2_dsr[16] -7.683 2.405 -13.179 -7.401 -3.942
beta3_dsr[11] 43.691 0.515 43.193 43.543 44.954
beta3_dsr[12] 33.936 0.856 31.996 34.079 34.806
beta3_dsr[13] 43.250 0.276 42.797 43.197 43.875
beta3_dsr[14] 43.389 0.251 43.081 43.321 43.969
beta3_dsr[15] 43.505 0.184 43.176 43.501 43.844
beta3_dsr[16] 43.445 0.159 43.170 43.436 43.759
beta4_dsr[11] 0.561 0.215 0.136 0.558 0.985
beta4_dsr[12] 0.232 0.439 -0.612 0.237 1.080
beta4_dsr[13] -0.169 0.220 -0.609 -0.163 0.246
beta4_dsr[14] 0.157 0.251 -0.335 0.156 0.650
beta4_dsr[15] 0.686 0.218 0.263 0.690 1.124
beta4_dsr[16] 0.153 0.228 -0.297 0.149 0.596
beta0_slope[11] -1.909 0.173 -2.257 -1.911 -1.583
beta0_slope[12] -4.696 0.268 -5.233 -4.689 -4.192
beta0_slope[13] -1.374 0.268 -2.116 -1.338 -0.972
beta0_slope[14] -2.638 0.181 -2.996 -2.636 -2.293
beta0_slope[15] -1.345 0.178 -1.681 -1.344 -0.988
beta0_slope[16] -2.713 0.179 -3.068 -2.712 -2.365
beta1_slope[11] 4.586 0.308 3.980 4.586 5.193
beta1_slope[12] 5.031 0.524 4.070 5.025 6.089
beta1_slope[13] 3.121 0.756 2.231 2.938 5.421
beta1_slope[14] 6.569 0.573 5.489 6.559 7.697
beta1_slope[15] 3.058 0.291 2.483 3.058 3.628
beta1_slope[16] 5.388 0.398 4.640 5.380 6.182
beta2_slope[11] 6.743 2.675 2.654 6.309 12.660
beta2_slope[12] 6.497 2.486 2.334 6.182 12.265
beta2_slope[13] 4.680 2.959 0.284 4.670 10.612
beta2_slope[14] 6.011 2.313 2.294 5.770 11.165
beta2_slope[15] 6.974 2.426 3.189 6.612 12.578
beta2_slope[16] 7.040 2.309 3.458 6.696 12.432
beta3_slope[11] 43.478 0.143 43.219 43.473 43.769
beta3_slope[12] 43.404 0.233 43.044 43.376 43.870
beta3_slope[13] 43.691 0.511 42.827 43.738 44.970
beta3_slope[14] 43.338 0.173 43.104 43.301 43.754
beta3_slope[15] 43.525 0.190 43.166 43.525 43.877
beta3_slope[16] 43.461 0.165 43.171 43.450 43.797
beta4_slope[11] -0.605 0.221 -1.034 -0.606 -0.181
beta4_slope[12] -1.396 0.656 -2.845 -1.327 -0.326
beta4_slope[13] 0.038 0.227 -0.403 0.036 0.480
beta4_slope[14] -0.189 0.260 -0.683 -0.198 0.309
beta4_slope[15] -0.754 0.225 -1.192 -0.750 -0.320
beta4_slope[16] -0.217 0.239 -0.669 -0.222 0.263
sigma_H[1] 0.202 0.059 0.101 0.197 0.331
sigma_H[2] 0.172 0.030 0.118 0.169 0.239
sigma_H[3] 0.200 0.043 0.129 0.197 0.295
sigma_H[4] 0.389 0.072 0.271 0.381 0.557
sigma_H[5] 0.995 0.230 0.585 0.983 1.472
sigma_H[6] 0.292 0.189 0.010 0.270 0.715
sigma_H[7] 0.283 0.052 0.198 0.278 0.400
sigma_H[8] 0.450 0.117 0.307 0.428 0.710
sigma_H[9] 0.421 0.090 0.287 0.409 0.634
sigma_H[10] 0.228 0.045 0.148 0.224 0.326
sigma_H[11] 0.280 0.047 0.200 0.276 0.382
sigma_H[12] 0.465 0.172 0.212 0.460 0.793
sigma_H[13] 0.199 0.037 0.134 0.197 0.277
sigma_H[14] 0.455 0.087 0.309 0.446 0.643
sigma_H[15] 0.248 0.042 0.178 0.245 0.339
sigma_H[16] 0.250 0.048 0.175 0.244 0.364
lambda_H[1] 3.036 4.183 0.151 1.611 14.013
lambda_H[2] 8.971 8.807 0.903 6.389 32.160
lambda_H[3] 6.817 9.560 0.307 3.598 33.174
lambda_H[4] 0.007 0.005 0.001 0.006 0.020
lambda_H[5] 2.638 7.555 0.015 0.335 23.865
lambda_H[6] 7.343 16.758 0.010 1.366 45.696
lambda_H[7] 0.014 0.010 0.002 0.012 0.040
lambda_H[8] 3.589 8.328 0.000 0.005 27.067
lambda_H[9] 0.019 0.014 0.004 0.016 0.054
lambda_H[10] 0.347 1.060 0.031 0.189 1.396
lambda_H[11] 0.365 0.646 0.015 0.198 1.610
lambda_H[12] 6.248 8.448 0.352 3.611 26.515
lambda_H[13] 4.244 3.725 0.314 3.192 14.359
lambda_H[14] 3.551 3.951 0.291 2.399 13.947
lambda_H[15] 0.032 0.081 0.004 0.019 0.129
lambda_H[16] 3.235 3.988 0.172 1.893 15.273
mu_lambda_H[1] 4.380 1.873 1.274 4.234 8.483
mu_lambda_H[2] 3.375 1.944 0.244 3.191 7.393
mu_lambda_H[3] 3.882 1.843 1.094 3.572 8.099
sigma_lambda_H[1] 8.773 4.302 2.050 8.252 18.436
sigma_lambda_H[2] 7.843 4.865 0.377 7.280 18.092
sigma_lambda_H[3] 6.564 3.837 1.387 5.842 16.159
beta_H[1,1] 6.834 1.080 4.372 7.017 8.487
beta_H[2,1] 9.858 0.463 8.862 9.887 10.729
beta_H[3,1] 8.012 0.753 6.249 8.106 9.221
beta_H[4,1] 11.042 7.665 -4.122 11.157 25.780
beta_H[5,1] -0.053 3.155 -6.526 0.077 6.038
beta_H[6,1] 3.389 3.675 -5.837 4.593 7.540
beta_H[7,1] 1.314 5.443 -10.375 1.653 11.086
beta_H[8,1] 24.421 24.584 -2.150 19.876 66.556
beta_H[9,1] 13.781 5.334 3.155 13.477 24.950
beta_H[10,1] 7.192 1.708 3.736 7.240 10.598
beta_H[11,1] 5.994 3.101 -1.362 6.796 10.003
beta_H[12,1] 2.550 0.930 0.806 2.494 4.680
beta_H[13,1] 9.069 0.778 7.428 9.113 10.412
beta_H[14,1] 2.180 0.988 0.321 2.179 4.083
beta_H[15,1] -5.327 3.921 -12.463 -5.565 2.834
beta_H[16,1] 3.504 1.652 0.110 3.604 6.544
beta_H[1,2] 7.908 0.246 7.399 7.918 8.360
beta_H[2,2] 10.037 0.131 9.781 10.037 10.292
beta_H[3,2] 8.970 0.194 8.558 8.970 9.360
beta_H[4,2] 3.036 1.448 0.218 3.030 5.954
beta_H[5,2] 1.985 1.064 -0.056 1.997 4.073
beta_H[6,2] 5.809 1.032 3.441 5.973 7.464
beta_H[7,2] 2.422 1.035 0.598 2.370 4.650
beta_H[8,2] -2.427 5.613 -11.299 -2.762 4.245
beta_H[9,2] 2.932 1.016 0.942 2.965 4.858
beta_H[10,2] 8.131 0.350 7.399 8.144 8.759
beta_H[11,2] 9.607 0.564 8.798 9.488 10.931
beta_H[12,2] 3.950 0.354 3.277 3.951 4.669
beta_H[13,2] 9.188 0.225 8.762 9.179 9.652
beta_H[14,2] 4.063 0.344 3.393 4.057 4.743
beta_H[15,2] 11.234 0.704 9.819 11.255 12.537
beta_H[16,2] 5.382 0.825 3.686 5.402 6.948
beta_H[1,3] 8.532 0.248 8.097 8.512 9.045
beta_H[2,3] 10.129 0.113 9.915 10.127 10.360
beta_H[3,3] 9.672 0.162 9.369 9.666 10.007
beta_H[4,3] -1.820 0.907 -3.635 -1.819 -0.005
beta_H[5,3] 4.212 0.758 2.679 4.214 5.671
beta_H[6,3] 8.015 1.176 6.428 7.641 10.633
beta_H[7,3] -2.430 0.646 -3.705 -2.409 -1.210
beta_H[8,3] 7.919 2.536 4.845 8.296 11.862
beta_H[9,3] -1.914 0.685 -3.266 -1.919 -0.569
beta_H[10,3] 8.859 0.285 8.306 8.856 9.413
beta_H[11,3] 8.653 0.269 8.081 8.672 9.140
beta_H[12,3] 5.366 0.288 4.698 5.389 5.855
beta_H[13,3] 9.065 0.170 8.727 9.063 9.419
beta_H[14,3] 5.865 0.262 5.316 5.870 6.355
beta_H[15,3] 10.491 0.324 9.872 10.491 11.135
beta_H[16,3] 7.380 0.432 6.411 7.424 8.094
beta_H[1,4] 8.301 0.189 7.891 8.312 8.624
beta_H[2,4] 10.189 0.113 9.950 10.196 10.400
beta_H[3,4] 10.178 0.163 9.814 10.194 10.461
beta_H[4,4] 11.698 0.417 10.858 11.699 12.527
beta_H[5,4] 6.172 1.045 4.526 6.077 8.418
beta_H[6,4] 7.290 0.820 5.288 7.484 8.464
beta_H[7,4] 8.205 0.329 7.562 8.204 8.835
beta_H[8,4] 5.861 0.959 4.190 5.933 7.114
beta_H[9,4] 6.988 0.401 6.193 6.993 7.810
beta_H[10,4] 7.795 0.263 7.320 7.777 8.360
beta_H[11,4] 9.417 0.200 9.015 9.417 9.806
beta_H[12,4] 7.139 0.204 6.741 7.139 7.532
beta_H[13,4] 9.179 0.148 8.894 9.180 9.466
beta_H[14,4] 7.827 0.207 7.419 7.829 8.224
beta_H[15,4] 9.501 0.243 9.014 9.502 9.995
beta_H[16,4] 9.235 0.181 8.912 9.221 9.627
beta_H[1,5] 8.989 0.148 8.675 8.995 9.274
beta_H[2,5] 10.790 0.092 10.612 10.788 10.979
beta_H[3,5] 10.920 0.170 10.616 10.910 11.279
beta_H[4,5] 8.423 0.426 7.598 8.414 9.269
beta_H[5,5] 5.069 0.837 3.193 5.212 6.426
beta_H[6,5] 8.634 0.565 7.792 8.538 10.014
beta_H[7,5] 6.842 0.314 6.254 6.836 7.471
beta_H[8,5] 8.877 0.736 7.910 8.682 10.264
beta_H[9,5] 8.287 0.396 7.505 8.293 9.073
beta_H[10,5] 10.049 0.250 9.532 10.051 10.525
beta_H[11,5] 11.480 0.233 11.018 11.481 11.931
beta_H[12,5] 8.457 0.196 8.083 8.457 8.857
beta_H[13,5] 10.049 0.132 9.787 10.049 10.311
beta_H[14,5] 9.220 0.208 8.840 9.212 9.661
beta_H[15,5] 11.179 0.243 10.707 11.181 11.651
beta_H[16,5] 9.987 0.152 9.675 9.990 10.272
beta_H[1,6] 10.178 0.187 9.853 10.163 10.596
beta_H[2,6] 11.509 0.106 11.297 11.509 11.715
beta_H[3,6] 10.818 0.158 10.464 10.830 11.099
beta_H[4,6] 12.844 0.753 11.275 12.856 14.295
beta_H[5,6] 6.099 0.770 4.758 6.030 7.904
beta_H[6,6] 8.740 0.594 7.264 8.799 9.635
beta_H[7,6] 9.840 0.538 8.771 9.832 10.915
beta_H[8,6] 8.658 1.071 6.464 9.097 9.952
beta_H[9,6] 8.396 0.676 7.059 8.398 9.768
beta_H[10,6] 9.532 0.331 8.838 9.562 10.118
beta_H[11,6] 10.865 0.342 10.132 10.893 11.483
beta_H[12,6] 9.374 0.248 8.897 9.367 9.902
beta_H[13,6] 11.076 0.156 10.789 11.071 11.402
beta_H[14,6] 9.828 0.264 9.305 9.832 10.331
beta_H[15,6] 10.846 0.424 9.993 10.848 11.677
beta_H[16,6] 10.643 0.182 10.274 10.649 10.984
beta_H[1,7] 10.868 0.859 8.789 10.955 12.283
beta_H[2,7] 12.211 0.419 11.321 12.212 13.020
beta_H[3,7] 10.567 0.655 9.113 10.647 11.630
beta_H[4,7] 2.631 3.840 -4.619 2.556 10.365
beta_H[5,7] 7.036 2.618 2.708 6.697 13.354
beta_H[6,7] 9.157 2.081 4.544 9.217 13.814
beta_H[7,7] 10.734 2.739 5.119 10.741 16.069
beta_H[8,7] 14.451 4.716 9.020 12.121 24.951
beta_H[9,7] 4.602 3.479 -2.619 4.608 11.109
beta_H[10,7] 9.782 1.498 7.061 9.701 13.114
beta_H[11,7] 10.876 1.586 7.906 10.764 14.385
beta_H[12,7] 10.100 0.825 8.218 10.160 11.582
beta_H[13,7] 11.722 0.685 10.153 11.793 12.797
beta_H[14,7] 10.381 0.858 8.557 10.431 11.890
beta_H[15,7] 12.075 2.215 7.583 12.055 16.559
beta_H[16,7] 11.706 0.812 10.307 11.616 13.600
beta0_H[1] 8.663 13.335 -19.426 8.859 35.517
beta0_H[2] 10.722 6.141 -1.489 10.701 22.488
beta0_H[3] 10.129 9.210 -8.817 10.080 29.682
beta0_H[4] 11.124 173.430 -345.062 13.339 359.014
beta0_H[5] 3.404 40.633 -81.085 4.392 82.578
beta0_H[6] 5.983 44.158 -89.564 7.638 95.317
beta0_H[7] -1.722 131.906 -271.939 0.475 254.810
beta0_H[8] 8.683 288.038 -621.659 6.550 703.712
beta0_H[9] 5.433 108.718 -226.446 5.892 219.475
beta0_H[10] 8.590 34.578 -61.949 8.441 80.768
beta0_H[11] 8.872 42.355 -84.022 8.600 95.505
beta0_H[12] 6.448 8.943 -12.953 6.571 24.729
beta0_H[13] 9.969 10.018 -9.600 9.987 28.000
beta0_H[14] 6.922 10.250 -13.519 6.898 26.843
beta0_H[15] 3.999 99.401 -204.313 4.236 205.793
beta0_H[16] 8.122 12.600 -17.487 8.396 33.706